Good evening, @Bleully, how are you?
This question will vary from player to player. Most people I know who have already bought the BiS equipment and are starting to tier are leaving the boots for last. In the end, it will all depend on certain factors, like the hunt you're currently hunting, how long are you planning to stay there, because it's worthless to tier up a weapon that you'll not be using in 2~3 months if you change hunting places, if so it's better to tier your armor first.
For me, the ideal is: start with your main weapon, legs/helmet ( I'm giving preference to tier the legs first, but again, this can vary from player to player) all to tier 3, and finally the boots, which so far I haven't seen the need to upgrade it to tier 3, tier 2 is already very good enough.
I hope this can help you resolve this question. Have a great weekend!